1. ## "simple" math question

If cosA=cos B, then when does A=B? (Always, sometimes, never, infinite etc).

2. No. Counterexample:

$\displaystyle \cos(0)=\cos(2\pi)=1 \Rightarrow 0 \neq 2\pi$

If you work on the interval $\displaystyle \left[ 0, \pi \right]$, then $\displaystyle \cos(a)=\cos(b)\Rightarrow a=b$

3. So what is the answer.. Never or sometimes?

4. it is always the same when it is a sign identity

$\displaystyle \cos\left({\theta}\right) = \cos\left({-\theta}\right)$

since $\displaystyle \beta$ would just be a reflection of $\displaystyle \alpha$ off the x axis then

$\displaystyle \cos{\alpha} = \cos{\beta}$

example:

$\displaystyle \cos\left({\frac{\pi}{4}}\right) =\cos\left({-\frac{\pi}{4}}\right) = \frac{\sqrt{2}}{2}$